King Charles III's speech to the US Congress last week was a "high stakes" moment, a senior royal aide has said, but one that stayed true to the monarch's personal "conscience".

The state visit speech, in which the King urged US lawmakers to defend Ukraine and support Nato, was a "measure of how much he personally cares", said the Palace aide.

The speech has been widely applauded for its diplomatic skill in encouraging US President Donald Trump to defend democratic values against aggressors in a "volatile world".

Buckingham Palace has been reflecting on a trip that was the biggest diplomatic challenge of the King's reign.

The King had travelled against a background of political tension between the UK and the US, most recently over the government's decision to not get involved in the Iran war.

Addressing US Congress on Tuesday, the King used humour and charm, but delivered a surprisingly direct message about the need for the US to support democratic values.

"Everything that is in that speech is an observable fact. And so, I think we felt very comfortable with the King speaking as he did," said the royal aide, who said the monarch was guided by a sense of "truth" and "conscience".

The speech had been welcomed by US lawmakers in the Capitol building, with the King receiving 12 standing ovations.

On the personal chemistry between the King and US president, it was more positive than might have been expected, given the differences in the UK and US positions, suggested the royal aide.

"They get on very well... It's a pairing, sort of unlikely though it might be in many ways… I mean, given some of the issues that have presented themselves in the bilateral relationship, you'd think it might all be a bit tricky.

"But far from it. And the warmth that you see in public is absolutely the warmth you see in private. That meeting in the Oval Office, there was an awful lot of warmth and laughter," said the royal aide.

Ahead of the visit, a diplomatic challenge for the UK had been that Trump had been an enthusiastic fan of the King and the monarchy, but had criticised the UK's prime minister and its armed forces.

The state visit had sought to build back bridges between the UK and US, beyond the focus on the royals.

"It's not a competition between the King and the government," said the royal aide.

"The King is there to support the government, to help the government. It was at the government's request, of course, that he undertook this visit."

There were no press conferences during the state visit, but there were still diplomatic eyebrows raised over Trump having seemed to suggest that the King was closer to his own views on the war with Iran.

In his state dinner speech, Trump had said: "We have militarily defeated that particular opponent, and we're never going to let that opponent ever - Charles agrees with me even more than I do - we're never going to let that opponent have a nuclear weapon."

Buckingham Palace had smoothed that over, saying that was in line with the UK government's position on the non-proliferation of nuclear weapons.

But later the president continued to suggest that the King was supporting his line on Iran - on an issue that has caused friction between the UK government and the Trump administration.

"If that were up to him, he would have probably helped us with Iran," said the president, about his talks with the "great King".

There had been no comment from Buckingham Palace on that.

There had been a form of diplomatic nightcap at the end of the visit, with the announcement by Trump that US tariffs would be scrapped on whisky imports, which was seen as an important boost to the Scottish whisky industry.

Trump said the visiting royals "got me to do something that nobody else was able to do, without hardly even asking".

An opinion poll published by YouGov on Saturday, based on a sample of 4,500 people, suggests the UK public has been impressed by the King's performance in the US.

It found 74% thought the King had handled the state visit well, compared with 4% who thought he had handled it badly.

That is a big turn-around on polls ahead of the visit, which had found more people wanting to call off the trip, and widespread scepticism about its value.

Andrew Lownie, who has caused royal headaches with his biography of Andrew Mountbatten-Windsor, said about the positive response to the King's visit: "What's most astonishing is the reaction not just of monarchists but of British republicans.

"Given the public pessimism and foreboding that led up to the visit, this is a considerable triumph for the King," he said, in his Lownie Report newsletter.

In Saturday's New York Times, Maureen Dowd wrote: "The King deftly schooled Donald, and Donald took it because he has always been awed by the British royal family."

The senior royal aide said: "What looked like risk and challenge was also a phenomenal opportunity. One that was grasped in both hands by the King."

Sign up here to get the latest royal stories and analysis every week with our Royal Watch newsletter. Those outside the UK can sign up here.